Research Journal of Resent Sciences ________________________________________________Res. J. Recent Sci. Vol. 1(1), 33-39, Jan. (2012) International Science Congress Association 33 Hexagonal Geometrical Inclusion to Estimate Effective Thermal Conductivity (ETC) of Porous System and Suspension system Including the Effect of Natural Convection Selvakumar B., Prabhu Raja V., NandhaKumar R., Senthil Kumar A.P., Vignesh M.S., VivekSharma G.R., Karthikeyan P.2 Department of Mechanical Engineering PSG College of Technology, Coimbatore, INDIA Department of Automobile Engineering PSG College of Technology, Coimbatore, INDIA Available online at: www.isca.in (Received20thOctober 2011, revised 26th November 2011, accepted 10th December 2011)Abstract: In this present work, a numerical model of hexagonal geometrical inclusion is developed to estimate the Effective Thermal Conductivity (ETC) of the two-phase materials taking the natural convection into account. A 2-D Constant Cross Section of unit cell model is analyzed with 1-D and 2-D heat transfer using Computational Fluid Dynamics (CFD) software. Numerical analysis has been carried out by considering primary effects (Conductivity ratio, concentration) and secondary effects (natural convection) to estimate ETC of two phase materials. The developed hexagonal geometrical model also shows excellent agreement with the available experimental and analytical data. Keywords: Effective Thermal Conductivity (ETC), Hexagonal Inclusions, Unit-cell approach, Two-phase materials, Natural Convection. Introduction The need of ETC estimation of two-phase materials such as ceramics, soils, foams, porous materials, fiber reinforced materials and composites are becoming increasingly important in the technological development. Two phase material have different physical and chemical characteristics. The performance of the two-phase material is dependent on the ETC of the materials. As it is tedious to conduct experiments for studying the effect of the parameters like concentration of the dispersed phase, conductivity of the material of the particles, grain size and shape, contact area, radiations, pressure effect on ETC, a numerical model and theoretical expression is needed to predict the value of ETC. Various mechanisms of heat transfer is observed in two phase systems like solid-solid conduction at the point of contact, conductive heat transfer through the gas medium, radiation and convection in interstitial voids. Radiation is negligible at low temperatures and convective heat transfer can be neglected for Grash of Number 2500.Many research are trying to evaluate ETC of two phase materials by analytical and experimental methods, which is time consuming and costly. So, numerical models which are easy and huge availability of resources attract the researchers to predict the ETC numerically. The minimum and maximum bounds for predicting the thermal conductivity of the two phase system has been developed by Maxwell and phase inverted Maxwell models. The ETC must lie between these bounds for all ranges of concentration and conductivity ratio. The upper and lower limits to the conductivity of two-phase materials based on parallel and series resistance are available. Effective thermal conductivity of two phase material will be affected by the particle contact as well as the secondary parameters like thermal radiation, pressure dependence, particle flattening, shape and size distribution for cylindrical unit cell containing spherical inclusions. It is assumed in this model that the deformation of the flux field is taken only as a function of concentration, not as a function of the conductivity ratio is an important deficiency in this model. The effective thermal conductivity can be obtained algebraically for number of porous media by applying the lumped parameter method based on an electric resistance analogy. This method consists of choosing a unit cell, dividing the geometry under consideration into solid, fluid or composite layers (consisting of both fluid and solid), and assuming one-dimensional conduction in the direction of temperature gradient in the unit cell. A comprehensive conductivity model by considering the primary parameters based on unit cell and field solution approaches can be used to predict the ETC of various binary metallic mixtures with a high degree of accuracy. Analytically effective thermal conductivity of two phase materials of various materials with different geometrical inclusions can be estimated. The collocated parameter model based on the unit cell approach is more effective in estimating the effective thermal conductivity of the two-phase materials. Empirical correlations based on a finite element analysis can also be used to predict the thermal conductivity of Fiber Reinforced Composite Laminates (FRCL) and the other constituents. In this model, FRCL is cured at high pressures to prevent air voids. The collocated parameter models are used to evaluate the ETC of the two-phase materials including the effect of Research Journal of Recent Sciences ______ Vol. 1(1), 33-39, Jan. (2012) International Science Congress Association various inclusions in the unit cell. The algeb ar e derived using unit cell based isotherm approach for two dimensional spatially periodic medium. The geometry of the medium was considered as matrix of touching and non touching in- line square, circular, hexagon and octagon cylinders.The effect of Darcy number, fluid Prandtl number, and thermal conductivity ratio on the Nusselt number the effective thermal conductivity of two phase materials The study is conducted by using this parameters uniform porosity, hence = 0.4 and = 2.5 of thermal conductivity of packed beds with randomly distributed inclusions or pores based on the solutions of Laplaces heat conduction equation is also possible D formulation provides a means of predicting the fiber thermal conductivity in both of the longitudinal and transverse directions. T he transverse thermal conductivity of continuous reinforced compos ites containing a random fiber distribution with imperfect interfaces can be estimated finite-element analysis12. The three- dimensional numerical finite-difference methods are used to estimate the thermal conductivity of a composite with two or more constituents This model helps to understand how the relative quantities and distributions of the compo nent m sample, affect the whole sample conductivity Two (a) Hexagon cylinder, (b) Unit cell of Hexagon cylinder for 1 (c) Unit Heat flow ______ _________________________________ ______________ International Science Congress Association The algeb raic equations e derived using unit cell based isotherm approach for two dimensional spatially periodic medium. The geometry of the medium was considered as matrix of touching and non - line square, circular, hexagon and octagon effect of Darcy number, fluid Prandtl number, and thermal conductivity ratio on the Nusselt number affects the effective thermal conductivity of two phase materials . using this parameters assumes = 2.5 10. The prediction of thermal conductivity of packed beds with randomly distributed inclusions or pores based on the solutions of Laplaces heat conduction equation is also possible 11.The 3- D formulation provides a means of predicting the fiber thermal conductivity in both of the longitudinal and he transverse thermal conductivity of ites containing a random fiber can be estimated using dimensional numerical to estimate the thermal conductivity of a composite with two or more constituents . to understand how the relative quantities nent m aterials, within a sample, affect the whole sample conductivity 13.In this paper, a numerical model has been developed based on the isotherm unit cell approach, considering the effect of primary parameters such as concentration, conductivity ratio, contact ratio and secondary parameters such as natural convection for predicting the ETC of two validation of the model is carried by compared with available literature experimental data and conventional models for various types of two- phase m Numerical Modeling for Hexagonal geometrical Inclusions Based on Primary (concentration, conductivity ratio) and Secondary Parameters (as natural convection) to Estimate ETC of Two- Phase Materials The development of numerical model for estimati based on the material and structure is extremely important for thermal design and analysis of two resistance method is basic for the formulation of model. The main feature of the method is to assume one dimensional h eat conduction and two conduction in a unit cell. The unit cell is divided into three parallel layers, namely, solids, fluid or composite layers shown in Fig. 1 for hexagonal inclusion based on the analytical method follows. (a) (b) (c) Figure-1 Two -dimensional spatially periodic two-phase system (a) Hexagon cylinder, (b) Unit cell of Hexagon cylinder for 1 - D heat transfer, (c) Unit cell of Hexagon cylinder for 2-D heat transfer Heat flow Heat flow Heat flow ______________ _______Res. J. Recent Sci. 34 a numerical model has been developed based on the isotherm unit cell approach, considering the effect of primary parameters such as concentration, conductivity ratio, contact ratio and secondary parameters such as natural convection for predicting the ETC of two -phase materials. The validation of the model is carried by compared with available literature experimental data and conventional models for phase m aterials. Numerical Modeling for Hexagonal geometrical Inclusions Based on Primary (concentration, conductivity ratio) and Secondary Parameters (as natural convection) to Estimate Phase Materials The development of numerical model for estimati ng the ETC based on the material and structure is extremely important for thermal design and analysis of two -phase systems. The resistance method is basic for the formulation of numerical The main feature of the method is to assume one - eat conduction and two -dimensional heat conduction in a unit cell. The unit cell is divided into three parallel layers, namely, solids, fluid or composite layers shown in Fig. 1 for hexagonal inclusion . The ETC equation based on the analytical method for hexagon cylinder is as D heat transfer, Research Journal of Recent Sciences ____________________________________________________________Res. J. Recent Sci. Vol. 1(1), 33-39, Jan. (2012) International Science Congress Association 35 () () () () () () () 233-13 sf2sf33-+23231--+3-effK==3-+231sf211231--+3--eel-el \n \n el  \n+ \n  el \n\n () sf3\r-el  \n\n (2.1) Numerical modelling for hexagonal Inclusions is shown in Figure-1 The assumption in this work is that the two phase media is stagnant and thermal conductivity is considered to be stagnant thermal conductivity11. The Business approximation is applied in the numerical modeling to take density difference into account. Two phase medium is considered to be isotropic, saturated with single phase fluid and the fluid is always in local thermal equilibrium with the solid matrix. All the calculations in the present study have been carried out using a commercial solver called FLUENT by considering the equation-2.1. Boundary Conditions: Wall boundary conditions: The velocity components at the wall are set to a no slip boundary condition. The components of velocity (u, v) are zero on the impermeable wall initially at time t=0.u, v = 0: ( 2.2) Surface of heater is subjected to a constant heat flux condition. q= constant ( 2.3) Outer wall is subjected to adiabatic condition, = 0 ( 2.4) Interface Conditions: The interface conditions between the fluid and solid medium using continuity in temperature, pressure, and heat flux. Grid independence Study and Validation test: Grid independence tests were conducted for the case of a unit cell model of 2-D with 1D and 2D heat transfer analysis. Hexagonal cylinder with conductivity ratio =20 and concentration =0.1, is taken for study of grid independence. In this regard, three iterations have been carried out for this case. The mesh size was changed from very coarse to very fine, (14400, 90000, and 146500) when performing the iterations. In each of these three runs, the average temperature throughout the length of wall was obtained and plotted as shown in figure-2. The results show that the variation of 14400 and 90000 cells is nearly 2.5%, where as the variation between 90000 and 146500 cells is less than 1%. So the mesh size of 90,000 was used in rest of the iterations. The validation test is carried out by simulating a simple non-linear 1D analysis along the thickness of the unit cell to obtain the temperature distribution. This solution agrees with the analytical result. The meshed surface of Hexagonal cylinder is shown in the figure-3. ` Figure-2: Grid independence study   \n \n \n \n  \n \r \n \r    Research Journal of Recent Sciences ______ Vol. 1(1), 33-39, Jan. 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ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　 &#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　n.`V,3G;'W BYn.`V,3G;'W BY&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　sB޻19ZSJ1VkUJ9*ƘRz&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　ֈJ?&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&Eə 5$ğ*%3UD"42jLh Ȅ&Lh ;k. EI Q Q q 1230 1338.67 m 1746 1338.67 l 1746 1336.67 l 1230 1336.67 l h W n q 2584 0 0 2 1230 1336.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP&Eə 5$ğ*%3UD"42jLh Ȅ&Lh ;k. EI Q Q q 1230 1338.67 m 1746 1338.67 l 1746 1336.67 l 1230 1336.67 l h W n q 2584 0 0 2 1230 1336.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP&Eə 5$ğ*%3UD"42jLh Ȅ&Lh ;k. EI Q Q q 1230 1338.67 m 1746 1338.67 l 1746 1336.67 l 1230 1336.67 l h W n q 2584 0 0 2 1230 1336.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　Ю- @D#L[@jܹs֭caar7l0wܤ$V0&d_~lccC/'&N*}IȀ wwwxfzR Cj@;99U7&@-Ffg"40[b`IW EI Q Q q 1230 1304.67 m 1746 1304.67 l 1746 1302.67 l 1230 1302.67 l h W n q 2584 0 0 2 1230 1302.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　Ю- @D#L[@jܹs֭caar7l0wܤ$V0&d_~lccC/'&N*}IȀ wwwxfzR Cj@;99U7&@-Ffg"40[b`IW EI Q Q q 1230 1304.67 m 1746 1304.67 l 1746 1302.67 l 1230 1302.67 l h W n q 2584 0 0 2 1230 1302.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DPЮ- @D#L[@jܹs֭caar7l0wܤ$V0&d_~lccC/'&N*}IȀ wwwxfzR Cj@;99U7&@-Ffg"40[b`IW EI Q Q q 1230 1304.67 m 1746 1304.67 l 1746 1302.67 l 1230 1302.67 l h W n q 2584 0 0 2 1230 1302.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x{;&#x@;&#xր;&#x;&#x;wo;&#x; �&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x{;&#x@;&#xր;&#x;&#x;wo;&#x; �&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#xx;&#xg;&#xm;&#x;&#x۷o;&#x@o;&#xy;&#x&;&#xK;&#x@ab;&#x8h;&#xhhhl;&#xl;&#xS;@Ӕ EI Q Q q 1230 1296.67 m 1746 1296.67 l 1746 1294.67 l 1230 1294.67 l h W n q 2584 0 0 2 1230 1294.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　L @e6l8|]J?@yYbEdduXXXhXz2aҤIpL @e6l8|]J?@yYbEdduXXXhXz2aҤIp&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　L @e6l8|]J?@yYbEdduXXXhXz2aҤIpxg=MK@y: -=@J__uֱ4T&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　xg=MK@y: -=@J__uֱ4T&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　xg=MK@y: -=@J__uֱ4T&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　L$,@H!ȅ͛7988fZR+&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　L$,@H!ȅ͛7988fZR+&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　L$,@H!ȅ͛7988fZR+L$,@H!ȅ͛7988fZR+&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x{;&#x";�&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　RTT{&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　`Q0 %hoo EI Q Q q 1230 1228.67 m 1746 1228.67 l 1746 1226.67 l 1230 1226.67 l h W n q 2584 0 0 2 1230 1226.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP`Q0 %hoo EI Q Q q 1230 1228.67 m 1746 1228.67 l 1746 1226.67 l 1230 1226.67 l h W n q 2584 0 0 2 1230 1226.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP`Q0 %hoo EI Q Q q 1230 1228.67 m 1746 1228.67 l 1746 1226.67 l 1230 1226.67 l h W n q 2584 0 0 2 1230 1226.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　#TZ:G`t+P^'cAmۆyRJksRVcuvƸ}S&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　______ _________________________________ ______________ International Science Congress Association Figure-3 Meshed surface for Hexagonal CylinderFigure 4 Comparison between Numerical (with convection) and Analytical ETC/K f for Conductivity ratio = 20 for Hexagon cylinder Figure 5 between Numerical (with convection) and Analytical ETC/K f for Conductivity ratio T*S-X5RGǫx*JI&#xw:;&#xt;&#x:;T*S-X5RGǫx*JIAРw6=tYI x߅ jvaj`0RYu!LzU&#x E;&#xܫR;&#xs;&#x";&#xǬ00;&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x;&#xwݭ;&#xV=;&#x;&#xP00;&#x;&#xwݭ;&#xV=;&#x;&#xP00;tzОN']aXJZآ`2ӉA�&#x;&#xj;&#xx;&#x ;&#x;&#x+#Ȕ;&#x_;&#x ;&#x|00;@p8[iröd  x 62G &#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　�L0;�L0;�L0;�L0;�L0;YT.^q!iCٓ QR1'1Ͻ7!v- 詫Qli,t:TR&#x{&;&#xj ;&#x;&#xT;&#xU;&#x`0 0;&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x+;&#xpܷ;�&#x+;&#xpܷ;�&#xh4;&#x;&#xz;&#xV ;&#xs00;&#xh4;&#x;&#xz;&#xV ;&#xs00;zRA@hr_x~LJ@B9 EI Q Q q 1746 1396.67 m 3491 1396.67 l 3491 1394.67 l 1746 1394.67 l h W n q 2584 0 0 2 1230 1394.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DPzRA@hr_x~LJ@B9 EI Q Q q 1746 1396.67 m 3491 1396.67 l 3491 1394.67 l 1746 1394.67 l h W n q 2584 0 0 2 1230 1394.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP&#xh4;&#x;&#xz;&#xV ;&#xs00;&#xh4;&#x;&#xz;&#xV ;&#xs00;&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　 =%$b3;7xB!b,ɑ]vU*zeHO ^ٖ˥ Ȧ`8G:Q*ύÀFgM[dGR@b=:ZB1 xnL{ B@`TaؾF2%GÊlFKrd2MME^eB n^C8nχKd~_@]ԏu@5_1~ $ EI Q Q q 1746 1394.67 m 3491 1394.67 l 3491 1392.67 l 1746 1392.67 l h W n q 2584 0 0 2 1230 1392.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP =%$b3;7xB!b,ɑ]vU*zeHO ^ٖ˥ Ȧ`8G:Q*ύÀFgM[dGR@b=:ZB1 xnL{ B@`TaؾF2%GÊlFKrd2MME^eB n^C8nχKd~_@]ԏu@5_1~ $ EI Q Q q 1746 1394.67 m 3491 1394.67 l 3491 1392.67 l 1746 1392.67 l h W n q 2584 0 0 2 1230 1392.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP&#xOB;&#x=TJ;&#xă;&#x}N;&#xJ;&#xj=;&#xN ;&#x|;&#x5h;&#xyv,;&#xLTW;&#xi;&#xV;&#x"; ;&#x'B2`;&#xr;&#xL&;&#x|000;&#xOB;&#x=TJ;&#xă;&#x}N;&#xJ;&#xj=;&#xN ;&#x|;&#x5h;&#xyv,;&#xLTW;&#xi;&#xV;&#x"; ;&#x'B2`;&#xr;&#xL&;&#x|000;&#xOB;&#x=TJ;&#xă;&#x}N;&#xJ;&#xj=;&#xN ;&#x|;&#x5h;&#xyv,;&#xLTW;&#xi;&#xV;&#x"; ;&#x'B2`;&#xr;&#xL&;&#x|000;&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　¶};&#x;&#xj,;&#x;&#xl; ";&#x[ױ;&#xV;#;&#xJq;&#xp;ó&#xݎ';&#xG@ ;&#xqv;&#xv;&#xzw:;&#x;&#xjr;&#xL&;&#xH;&#x_1;&#xk;&#xG"; %H;&#xj;&#x;-;&#xt:;X,; zP;&#xh;&#xP00;R7{L]$ǑV+:5,=h05FkRF@0/"3 t8 BDJ?¶};&#x;&#xj,;&#x;&#xl; ";&#x[ױ;&#xV;#;&#xJq;&#xp;ó&#xݎ';&#xG@ ;&#xqv;&#xv;&#xzw:;&#x;&#xjr;&#xL&;&#xH;&#x_1;&#xk;&#xG"; %H;&#xj;&#x;-;&#xt:;X,; zP;&#xh;&#xP00;&#x!B;&#xW*@;&#x ;&#x-q9;&#x;&#x;&#xth;&#x ;&#xޡ6; 5~;&#xv;&#xÿ;&#x;&#xu;&#x=؛;&#x; ^;&#xws;Ä;&#x;&#xZT;&#x ;&#x` N;&#xAT;&#x}o8;&#xp#;&#x;b0;&#x!B;&#xW*@;&#x ;&#x-q9;&#x;&#x;&#xth;&#x ;&#xޡ6; 5~;&#xv;&#xÿ;&#x;&#xu;&#x=؛;&#x; ^;&#xws;Ä;&#x;&#xZT;&#x ;&#x` N;&#xAT;&#x}o8;&#xp#;&#x;b0;&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　u:|l6dJ"Z-8Q*vHX,zF`.7m Ä90Ju:|l6dJ"Z-8Q*vHX,zF`.7m Ä90Ju:|l6dJ"Z-8Q*vHX,zF`.7m Ä90Ju:|l6dJ"Z-8Q*vHX,zF`.7m Ä90J&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　V#&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#xN8s;&#x;&#xجg;ö; ;&#xX00;&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　 $1Wϩ|/oy5susR ].R&#x*;&#x;&#x;&#x;&#xL;&#x;.7"x1;^_L&*ٯ&V+d&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　.7"x1;^_L&*ٯ&V+d&#xgy; &y;&#x};&#x;&#xL;&#x&k4;&#xv;&#xz;&#xNc;&#x;&#x,V;&#x;&#xr;&#xHF#;&#xv;&#x#" ;&#xǕ;&#xv;;&#x[V;";&#xp8N;&#x;&#xZ;&#x;&#x@R2;&#x;&#x`0;&#xT*; L;P;&#xp;&#xP=;&#xX,;&#x t:;&#x;&#xj;&#x|000;.7"x1;^_L&*ٯ&V+d&#x/H;&#x t#;&#xҨT*;&#x";ó;&#xl;&#xr;&#xr;&#x:Y;&#x&; j;&#xi000;.7"x1;^_L&*ٯ&V+d&#x/H;&#x t#;&#xҨT*;&#x";ó;&#xl;&#xr;&#xr;&#x:Y;&#x&; j;&#xi000;&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　`d$!rzGzߠ={C 2 B b+Nr4=M&Vn4Lۭ``b{^83H&˅UhhZF&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　`d$!rzGzߠ={C 2 B b+Nr4=M&Vn4Lۭ``b{^83H&˅UhhZF&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　`d$!rzGzߠ={C 2 B b+Nr4=M&Vn4Lۭ``b{^83H&˅UhhZF&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　: EI Q Q q 1746 1380.67 m 3491 1380.67 l 3491 1378.67 l 1746 1378.67 l h W n q 2584 0 0 2 1230 1378.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP: EI Q Q q 1746 1380.67 m 3491 1380.67 l 3491 1378.67 l 1746 1378.67 l h W n q 2584 0 0 2 1230 1378.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP: EI Q Q q 1746 1380.67 m 3491 1380.67 l 3491 1378.67 l 1746 1378.67 l h W n q 2584 0 0 2 1230 1378.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP: EI Q Q q 1746 1380.67 m 3491 1380.67 l 3491 1378.67 l 1746 1378.67 l h W n q 2584 0 0 2 1230 1378.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　z`wj5T5Aj/g4~|{d]Ȳsuj1vUrS 1v-z2&yőA Bv`0#L|F6㪘w AGvOHHH!?VĔ EI Q Q q 1746 1378.67 m 3491 1378.67 l 3491 1376.67 l 1746 1376.67 l h W n q 2584 0 0 2 1230 1376.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DPz`wj5T5Aj/g4~|{d]Ȳsuj1vUrS 1v-z2&yőA Bv`0#L|F6㪘w AGvOHHH!?VĔ EI Q Q q 1746 1378.67 m 3491 1378.67 l 3491 1376.67 l 1746 1376.67 l h W n q 2584 0 0 2 1230 1376.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DPz`wj5T5Aj/g4~|{d]Ȳsuj1vUrS 1v-z2&yőA Bv`0#L|F6㪘w AGvOHHH!?VĔ EI Q Q q 1746 1378.67 m 3491 1378.67 l 3491 1376.67 l 1746 1376.67 l h W n q 2584 0 0 2 1230 1376.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DPz`wj5T5Aj/g4~|{d]Ȳsuj1vUrS 1v-z2&yőA Bv`0#L|F6㪘w AGvOHHH!?VĔ EI Q Q q 1746 1378.67 m 3491 1378.67 l 3491 1376.67 l 1746 1376.67 l h W n q 2584 0 0 2 1230 1376.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　 &#x ;u:;&#x*OP;&#xU;&#xUV;&#x];
 m;|0; &#x ;u:;&#x*OP;&#xU;&#xUV;&#x];
 m;|0;&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　OOyADjQ=*K|o:&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#xòT;&#x5L;&#xTUe;&#xj;&#xr;&#xr$;&#xZ0;&#xòT;&#x5L;&#xTUe;&#xj;&#xr;&#xr$;&#xZ0;&#x;&#xv|0;jh p8D$h4VED4CΌs8m I5T ĀnA nbMm]B:ul&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　Q*£%+r{^z:.;*A$. ?𓊇 ddddd|p͔ EI Q Q q 1746 1370.67 m 3491 1370.67 l 3491 1368.67 l 1746 1368.67 l h W n q 2584 0 0 2 1230 1368.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP�#OFm;7�&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　 &#xMtZ;&#x#;&#x|0;&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　1H ߿WTT8qǏ@Ư_֬Y$***666_|yqVV.Z$ k׮}-"""##dɓ'&#x@q ;&#x߿@;&#xG;&#xet;&#x@l;&#xT;|&#x ̞=;&#x{ٲe;&#x;&#xh";&#xT;&#xsAv;&#xvk;&#xHU;&#x__O;&#x?~;&#xp;&#xs;�&#x@q ;&#x߿@;&#xG;&#xet;&#x@l;&#xT;|&#x ̞=;&#x{ٲe;&#x;&#xh";&#xT;&#xsAv;&#xvk;&#xHU;&#x__O;&#x?~;&#xp;&#xs;�&#x@q ;&#x߿@;&#xG;&#xet;&#x@l;&#xT;|&#x ̞=;&#x{ٲe;&#x;&#xh";&#xT;&#xsAv;&#xvk;&#xHU;&#x__O;&#x?~;&#xp;&#xs;�&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　`Q@uI" EI Q Q q 1746 1364.67 m 3491 1364.67 l 3491 1362.67 l 1746 1362.67 l h W n q 2584 0 0 2 1230 1362.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP`Q@uI" EI Q Q q 1746 1364.67 m 3491 1364.67 l 3491 1362.67 l 1746 1362.67 l h W n q 2584 0 0 2 1230 1362.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP&#x{;&#x]W4;&#xٹ;¢&#xy;&#xѰ;&#xm;;&#xl;&#x#;$5;&#xݻ;&#xl;l;&#xS;�&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　  &#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　 &#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　n.`V,3G;'W BYn.`V,3G;'W BY&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　sB޻19ZSJ1VkUJ9*ƘRz&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　ֈJ?&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&Eə 5$ğ*%3UD"42jLh Ȅ&Lh ;k. EI Q Q q 1746 1338.67 m 3491 1338.67 l 3491 1336.67 l 1746 1336.67 l h W n q 2584 0 0 2 1230 1336.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP&Eə 5$ğ*%3UD"42jLh Ȅ&Lh ;k. EI Q Q q 1746 1338.67 m 3491 1338.67 l 3491 1336.67 l 1746 1336.67 l h W n q 2584 0 0 2 1230 1336.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP&Eə 5$ğ*%3UD"42jLh Ȅ&Lh ;k. EI Q Q q 1746 1338.67 m 3491 1338.67 l 3491 1336.67 l 1746 1336.67 l h W n q 2584 0 0 2 1230 1336.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　Ю- @D#L[@jܹs֭caar7l0wܤ$V0&d_~lccC/'&N*}IȀ wwwxfzR Cj@;99U7&@-Ffg"40[b`IW EI Q Q q 1746 1304.67 m 3491 1304.67 l 3491 1302.67 l 1746 1302.67 l h W n q 2584 0 0 2 1230 1302.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　Ю- @D#L[@jܹs֭caar7l0wܤ$V0&d_~lccC/'&N*}IȀ wwwxfzR Cj@;99U7&@-Ffg"40[b`IW EI Q Q q 1746 1304.67 m 3491 1304.67 l 3491 1302.67 l 1746 1302.67 l h W n q 2584 0 0 2 1230 1302.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DPЮ- @D#L[@jܹs֭caar7l0wܤ$V0&d_~lccC/'&N*}IȀ wwwxfzR Cj@;99U7&@-Ffg"40[b`IW EI Q Q q 1746 1304.67 m 3491 1304.67 l 3491 1302.67 l 1746 1302.67 l h W n q 2584 0 0 2 1230 1302.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x{;&#x@;&#xր;&#x;&#x;wo;&#x; �&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x{;&#x@;&#xր;&#x;&#x;wo;&#x; �&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#xx;&#xg;&#xm;&#x;&#x۷o;&#x@o;&#xy;&#x&;&#xK;&#x@ab;&#x8h;&#xhhhl;&#xl;&#xS;@Ӕ EI Q Q q 1746 1296.67 m 3491 1296.67 l 3491 1294.67 l 1746 1294.67 l h W n q 2584 0 0 2 1230 1294.67 cm BI /CS/RGB /W 1292 /H 1 /BPC 8 /F/Fl /DP&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　L @e6l8|]J?@yYbEdduXXXhXz2aҤIpL @e6l8|]J?@yYbEdduXXXhXz2aҤIp&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　L @e6l8|]J?@yYbEdduXXXhXz2aҤIpxg=MK@y: -=@J__uֱ4T&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　xg=MK@y: -=@J__uֱ4T&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　xg=MK@y: -=@J__uֱ4T&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　L$,@H!ȅ͛7988fZR+&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　L$,@H!ȅ͛7988fZR+&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　L$,@H!ȅ͛7988fZR+L$,@H!ȅ͛7988fZR+&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x{;&#x";�&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　&#x/Pre; ict;&#xor 1; /C;&#xolum;&#xns 1;ʒ ;&#x/Col;&#xors ;　RTT{&#x/Pre; ict;&#xor 1; 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J. Recent Sci. 36 for Conductivity ratio for Conductivity ratio = 100 for Research Journal of Recent Sciences ____________________________________________________________Res. J. Recent Sci. Vol. 1(1), 33-39, Jan. (2012) International Science Congress Association 37 Results and Discussion Influence of concentration for Hexagonal geometrical inclusions including the effect of Natural Convection: The effect of concentration () on the non-dimensional thermal conductivity of two-dimensional geometrys for conductivity ratios ( = 20, 100) have been investigated taking the effect of natural convection into account. Hexagon cylinder: The hexagonal model lies between parallel and series lines for conductivity ratio () = 20,100 and contact ratio () = 0 to 0.2 as shown in figure-4 and figure-5. It also lies between Maxwell and Inverted-Maxwell models. This shows that the numerical modeling have good agreement with analytical model. Hexagonal model is not applicable beyond = 0.65 and 0.8 respectively, due to anisotropic shape property. It is the limitation of the hexagonal geometrical inclusions. From figure-4 and figure-5, the non-dimensional ETC with natural convection deviates from the ETC value determined analytically due to the convective heat transfer taking place in the fluid region. The dominance of fluid thermal conductivity is high for concentrations till = 0.7 - 0.8, but for higher concentrations, ( � 0.8) the solid thermal conductivity become more dominant than the fluid. This can be easily inferred from the figure-4 and figure-5 that the ETC value raises to the maximum for � 0.8. From the tables 1-2, numerical estimated one-dimensional (1-D) and two-dimensional (2-D) ETC with convection are compared with the available literature experimental values for hexagon inclusions. For porous systems, 2-D heat transfer shows 11.92% of deviation when compared to 12.38% deviation of 1-D heat transfer, i.e. more volume of fluid in the porous system causes, natural convection to occur. So in this case 2-D heat transfer is preferred. For suspension systems, the percentage of deviation is less for 1-D heat transfer (8.18%) when compared to 2-D transfer (12.07%) due to high value of conductivity ratio. Table-1 Comparison of results of numerical models with experimental data for hexagon cylinder porous system No. Sample (solid/fluid phase)14-24s W/m K f W/m K (k/k) expW/m K (c/a) hex W/mK 1 - D Heat flow 2 - D Heat flow CCSwc Devi CCSwc Devi 1 Glass sphere/ air 1.099 0.024 45.792 0.74 0.227 0.85 0.23 1.32 0.251 10.57 2 Glass sphere/air 1.099 0.024 45.792 0.2 0.041 0.05 0.04 17.07 0.048 18.29 3 Silica sphere/water 12.414 0.586 21.184 0.569 2.544 0.8 2.84 11.63 2.861 12.46 4 Stainless steel/ethyl alcohol 20.864 0.337 61.911 0.495 2.009 0.27 2.25 11.96 2.271 13.04 5 Glass sphere/ iso-octane 1.061 0.144 7.368 0.57 0.406 0.01 0.43 5.911 0.451 11.08 6 Lead shots/helium 34.347 0.147 233.65 0.62 2.14 0.16 2.31 7.94 2.33 8.87 7 Lead shots/hydrogen 34.347 0.179 191.88 0.62 2.429 0.18 2.82 16.09 2.841 16.96 8 Lead shots/water 34.347 0.627 54.78 0.62 5.404 0.6 5.45 0.85 5.471 1.23 9 Zircona powder/air 2.001 0.021 95.286 0.47 0.12 0.1 0.13 8.33 0.131 9.16 10 Lead/water 33.764 0.586 57.618 0.6 4.329 0.37 4.72 9.03 4.741 9.51 11 Zircona powder/air 2.001 0.03 66.7 0.58 0.23 0.32 0.26 13.05 0.281 22.17 12 Zircona powder/air 2.001 0.03 66.7 0.64 0.281 0.45 0.31 10.32 0.32 13.87 13 Zircona powder/air 2.001 0.03 66.7 0.7 0.364 0.75 0.39 7.14 0.41 12.63 14 Glass beads/ air 1.201 0.028 42.893 0.65 0.22 0.75 0.24 9.09 0.25 13.63 15 Glass beads/benzene 1.201 0.14 8.579 0.65 0.5 0.01 0.53 6 0.542 8.4 16 Quardz sand/water 5.003 0.62 8.069 0.676 2.331 0.1 2.16 7.33 2.172 6.82 17 Glass beads/air 1.091 0.029 37.621 0.6 0.18 0.6 0.19 5.55 0.202 12.22 18 Micro beads/air 1.046 0.026 40.231 0.65 0.193 0.7 0.20 7.25 0.219 13.47 19 Micro beads/soltrol 1.046 0.133 7.865 0.639 0.452 0.01 0.48 7.52 0.501 10.84 20 Wassau sand/ n-heptane 8.374 0.129 64.915 0.485 0.722 0.2 0.83 14.95 0.842 16.62 21 Ottawa sand/ helium 8.374 0.147 56.966 0.64 1.323 0.6 1.45 9.59 1.462 10.50 22 Wassau sand/ helium 8.374 0.147 56.966 0.41 0.598 0.15 0.61 2.00 0.622 4.013 23 Miami silt loam/air 2.932 0.023 127.48 0.456 0.169 0.15 0.18 6.50 0.192 13.60 24 Miami silt loam/air 2.932 0.023 127.48 0.552 0.221 0.2 0.24 8.59 0.252 14.02 25 Glass/air 1.13 0.026 43.462 0.6 0.176 0.4 0.2 13.63 0.201 14.20 Average Deviation 12.38 11.92 Research Journal of Recent Sciences ____________________________________________________________Res. J. Recent Sci. Vol. 1(1), 33-39, Jan. (2012) International Science Congress Association 38 Table-2 Comparison of results of numerical models with experimental data for hexagon cylinder suspension system No. Sample (solid/fluid phase)25-28s W/m K f W/m K (k/k) exp W/m K (c/a) k hex W/m K 1-D Heat flow 2-D Heat flow CCSwc Devi CCSwc Devi 1 Graphite/Water 160.03 0.66 241.01 0.05 0.83 0.009 0.92 10.84 0.95 14.45 2 Graphite/Water 160.03 0.66 241.01 0.11 1.13 0.02 1.26 11.50 1.28 13.27 3 Graphite/Water 160.03 0.66 241.01 0.17 1.44 0.02 1.52 5.55 1.55 7.63 4 Graphite/Water 160.03 0.66 241.01 0.24 1.92 0.02 2.05 6.77 2.18 13.54 5 Selenium/polypropylene Glycol 5.19 0.14 37.09 0.1 0.18 0.03 0.19 5.55 0.2 11.11 6 Selenium/polypropylene glycol 5.19 0.14 37.09 0.2 0.22 0.03 0.25 13.63 0.252 14.54 7 Selenium/polypropylene glycol 5.19 0.14 37.09 0.3 0.32 0.1 0.36 12.5 0.37 15.62 8 Selenium/polypropylene Glycol 5.19 0.14 37.09 0.4 0.42 0.13 0.45 7.14 0.462 10 9 Aluminum/water 204.24 0.66 310.86 0.06 0.76 0.005 0.77 1.31 0.798 5 10 Aluminum/water 204.24 0.66 310.86 0.12 0.97 0.007 1.05 8.24 1.12 15.46 11 Aluminum/water 204.24 0.66 310.86 0.18 1.4 0.007 1.32 5.71 1.52 8.57 12 Aluminum/water 204.24 0.66 310.86 0.21 1.81 0.02 2.02 11.60 2.12 17.12 13 Graphite/Water 160.94 0.56 286.37 0.16 1.19 0.02 1.24 4.20 1.27 6.72 14 Zinc sulphate/lard 0.61 0.2 3.11 0.38 0.31 0.001 0.34 9.67 0.36 16.12 15 Zinc sulphate/lard 0.61 0.2 3.11 0.56 0.35 0.001 0.38 8.57 0.401 14.57 16 Marble/Vaselene 2.98 0.19 16.09 0.6 0.75 0.002 0.79 5.33 0.82 9.33 Conclusion The effects of concentration, conductivity ratio on the ETC of hexagon geometrical inclusions have been investigated with the effect of natural convection. The numerical models are also compared with available experimental data. The results show that for the porous system, 2-D heat flow is more accurate than 1-D heat flow to estimate ETC. In emulsion system, I-D heat flow is better than 2-D heat flow. Nomenclature: a Length of the square, hexagon and octagon cylinders or Diameter of the circular cylinder, A Wall area (m), c Width Of the connecting plate in the square, circular, hexagon and octagon cylinders, Cp Specific heat Capacity, kJ/kg K, CCSwc Constant Cross Section with convection, CR Contact Ratio, Devi Deviation, ETC (A) Analytical Effective ThermalConductivity (W/m K), ETC (E) Empirical Effective Thermal Conductivity (W/m K), ETC (NWC) Numerical Effective Thermal Conductivity with Natural Convection (W/m K), keff Effective thermal conductivity of two-phase materials, (W/m K), kf Fluid or continuous thermal conductivity, (W/m K), ks Solid or dispersed thermal conductivity, (W/m K), Ksf Equivalent thermal conductivity of a composite layer, (W/m K), l Length of the unit cell, (m), n Adiabatic Index q Heat Flux, (W/m), T Temperature, (K), u X component of velocity (m/s), v Y component of velocity (m/s), WC With Natural Convection. 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